基于能量原理的弹性地基梁底面摩阻效应分析

Analysis on Underside Friction Effect of Beam on Elastic Foundation Based on Energy Principle

针对Winkler地基模型不能考虑梁与地基底面摩阻效应的不足,在地基与梁底接触面上引入一系列各自独立的水平弹簧,假定弹簧反力即切向摩阻力与梁底和地基间的切向相对位移成正比,从能量角度出发,基于最小势能原理,建立考虑底面摩阻效应的弹性地基梁能量方程,并引入位移形函数进行求解,导出对称载荷条件下考虑切向摩阻力作用时地基梁位移及内力解答。最后通过地基梁计算实例分析,验证该解答的正确性和合理性,并对相关计算参数进行深入探讨。计算结果表明:切向摩阻力沿梁长呈非线性分布,其对地基梁挠度及弯矩计算的影响较大,而对剪力的影响并不强烈。

A series of separate horizontal springs were roduced between beam and subgrade in view of the fact that the Winkler foundation model was unable to consider the friction effect between beam bottom and subgrade. The horizontal counter forces of spring named the tangential friction forces were assumed to be in direct proportion to relative tangential displacements between beam bottom and subgrade. From the standpoint of energy and on the principle of the minimum potential energy, the energy equations for beam on elastic foundation considering underside friction effect were established. The equations were solved by the displacement shape function. The displacements and internal forces of beam on elastic foundation were derived under action of tan gential friction forces and symmetrical loading. The validity and rationality of the solutions were verified by cal- culation examples. Correlative calculation parameters were also discussed deeply. The results show that tangential friction forces distribute along the beam nonlinearly and they have intense influence on the deflection and bending moment of beam and have no intense influence on shearing forces.